Question

$P_A^0$ and $P_B^0$ are the vapour pressure of pure liquid components, $A$ and $B$, respectively of an ideal binary solution. If $X_A$ represents the mole fraction of component $A$, the total pressure of the solution will be:

• A. $P_B^0+X_A(P_B^0-P_A^0)$
• B. $P_B^0+X_A(P_A^0-P_B^0)$
• C. $P_A^0+X_A(P_B^0-P_A^0)$
• D. $P_A^0+X_A(P_A^0-P_B^0)$

Answer 1

The correct option is B $P_B^0+X_A(P_A^0-P_B^0)$

Raoult's law of vapour pressure,
$P_S=P_B^0{X}_A+P_B^0{X}_B{X}_A+X_B=1$
On substituting the value of $X_B$ in vapour pressure formula,
$X_B=1-X_A{P}_S=P_A^0{X}_A+P_B^0(1-X_A)P_S=P_A^0{X}_A+P_B^0-P_B^0{X}_A{P}_S=X_A(P_A^0-P_B^0)+P_B^0$
Therefore, the correct answer is (B).